Internal problem ID [2865]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 116.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\sin \relax (x ) \left (\csc \relax (y)-\cot \relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve(diff(y(x),x) = sin(x)*(csc(y(x))-cot(y(x))),y(x), singsol=all)
\[ y \relax (x ) = \arccos \left ({\mathrm e}^{-\cos \relax (x )} c_{1}+1\right ) \]
✓ Solution by Mathematica
Time used: 8.221 (sec). Leaf size: 26
DSolve[y'[x]==Sin[x](Csc[y[x]]-Cot[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {ArcSin}\left (e^{\frac {1}{4} (-2 \cos (x)+c_1)}\right ) \\ y(x)\to 0 \\ \end{align*}